Search

Abstract: We study a family of orthogonal polynomials which generalizes a sequence of polynomials considered by L. Carlitz. We show that they are a special case of the Sheffer polynomials and point out some interesting connections with certain Sobolev orthogonal polynomials. [Copyright &y& Elsevier]

Let r ≥ 2 and r be even. An r -hypergraph G on n vertices is called odd-colorable if there exists a map φ : [ n ] → [ r ] such that for any edge { j 1 , j 2 , … , j r } of G , we have φ ( j 1 ) + φ ( j 2 ) + ⋅ ⋯ ⋅ + φ ( j r ) ≡ r ∕ 2 ( mod r ) . In this paper, we first determine that, if r = 2 q ( 2 t + 1 ) and n ≥ 2 q ( 2 q − 1 ) r , then the maximum chromatic number in the class of the odd-colorable r -hypergraphs on n vertices is 2 q , which answers a question raised by V. Nikiforov recently in Nikiforov (2017). We also study some applications of the spectral symmetry of the odd-colorable r -hypergraphs given in the same paper by V. Nikiforov. We show that the Laplacian spectrum S p e c ( L ( G ) ) and the signless Laplacian spectrum S p e c ( Q ( G ) ) of an r -hypergraph G are equal if and only if r is even and G is odd-colorable. As an application of this result, we give an affirmative answer for the remaining unsolved case r ⁄ ≡ 0 ( m o d 4 ) of a question raised in Shao et al. (2015) about whether S p e c ( L ( G ) ) = S p e c ( Q ( G ) ) implies that L ( G ) and Q ( G ) have the same H-spectrum. [ABSTRACT FROM AUTHOR]

This is a survey or exposition of a particular collection of results and open problems involving snarks — simple “cubic” (3-valent) graphs for which, for nontrivial reasons, the edges cannot be 3-colored. The results and problems here are rooted in a series of papers by László Kászonyi that were published in the early 1970s. The problems posed in this survey paper can be tackled without too much specialized mathematical preparation, and in particular seem well suited for interested undergraduate mathematics students to pursue as independent research projects. This survey paper is intended to facilitate research on these problems. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we apply a complete pivoting strategy to compute the left-looking version of AINV preconditioner for linear systems. As the preprocessing, the MultiLevel Nested Dissection reordering has also been applied. We have used this preconditioner as the right preconditioner for several linear systems where the coefficient matrices have been downloaded from the University of Florida Sparse Matrix Collection. Numerical experiments presented in this paper indicate the effectiveness of such a complete pivoting on the quality of left-looking version of AINV preconditioner. [Copyright &y& Elsevier]

Abstract: In this paper, the bases of a semimodule over a commutative semiring R are investigated. Some properties and characterizations of the bases are discussed and some equivalent conditions for a basis to be a free basis in a finitely generated free semimodule over R are given. The different possible cardinalities for a basis in a finitely generated free semimodule over R are considered and some equivalent descriptions are obtained for a commutative semiring R satisfying the property that any two bases for a finitely generated free R-semimodule have the same cardinality. Partial results obtained in the paper develop and generalize the corresponding results for commutative join-semirings and for commutative zerosumfree semirings. [Copyright &y& Elsevier]

Abstract: In this paper, we study the basic homogeneous -machine scheduling problem where weakly dependent unit-time jobs have to be scheduled within the time windows between their release dates and due dates so that, for any subset of machines, the set of the time units at which at least one machine is busy, is in interval. We first introduce the notions of pyramidal structure, -hole, -matching, preschedule, -schedule and schedule for this problem. Then we provide a feasibility criteria for a preschedule. The key result of the paper is then to provide a structural necessary and sufficient condition for an instance of the problem to be feasible. We conclude by giving the directions of ongoing works and by bringing open questions related to different variants of the basic non-idling -machine scheduling problem. [Copyright &y& Elsevier]

Abstract: Let be a family of subsets of an -element set. Sperner’s theorem says that if there is no inclusion among the members of then the largest family under this condition is the one containing all -element subsets. The present paper surveys certain generalizations of this theorem. The maximum size of is to be found under the condition that a certain configuration is excluded. The configuration here is always described by inclusions. More formally, let be a poset. The maximum size of a family which does not contain as a (not-necessarily induced) subposet is denoted by . The paper is based on a lecture of the author at the Jubilee Conference on Discrete Mathematics [Banasthali University, January 11–13, 2009], but it was somewhat updated in December 2010. [Copyright &y& Elsevier]

Abstract: The family of all the submanifolds of a given Riemannian or pseudo-Riemannian manifold is large enough to classify them into some interesting subfamilies such as minimal (maximal), totally geodesic, Einstein, etc. Most of these have been extensively studied by many authors, but as far as we know, no paper has hitherto been published on the class of isotropic submanifolds. The purpose of this paper is therefore to gain a better understanding of this interesting class of submanifolds that arise naturally in mathematics and physics by studying their relationships with other closely distinguished families. [Copyright &y& Elsevier]

Abstract: This paper is mainly concerned with the structure of the centre of a vector lattice. A special attention is paid in the case when , . In this paper we give some characterizations of dense vector sublattices of the centre. Those characterizations will be applied in several directions. At the end of this work we compare various fullness and richness properties of the centre of a vector lattice. [Copyright &y& Elsevier]

Abstract: The rank of a graph G is defined to be the rank of its adjacency matrix. In this paper, we consider the following problem: what is the structure of a connected graph G with rank 5? or equivalently, what is the structure of a connected n-vertex graph G whose adjacency matrix has nullity ? In this paper, we completely characterize connected graphs G whose adjacency matrix has rank 5. [Copyright &y& Elsevier]

Abstract: Recently Takahashi has introduced James type constant. In this paper, we will introduce some new properties of the constant such as monotonicity, uniform non-squareness characterized by James type constant, and so on. We also investigate some relations between James type constant and other constants. Our main results of the paper are three examples of the constant. These examples include , and space, where is the space with the norm . We calculate exact values of James type constant in these concrete spaces. [Copyright &y& Elsevier]

Abstract: Let be a connected graph and , where and stand for the Wiener and Szeged numbers of , respectively. A well-known result of Klavžar, Rajapakse and Gutman states that and by a result of Dobrynin and Gutman if and only if each block of is complete. In an earlier paper a classification of graphs with is presented. In this paper, we continue our earlier work to classify connected graphs which satisfy or . [Copyright &y& Elsevier]

Abstract Given a finite group G , we say that G has property P n if for every prime integer p , G has at most n − 1 irreducible characters whose degrees are multiples of p. In this paper, we classify all finite groups that have property P 4. We show that the groups satisfying property P 4 are exactly the finite groups with at most three nonlinear irreducible characters, one solvable group of order 168, SL 2 (3) , A 5 , S 5 , PSL 2 (7) and A 6. [ABSTRACT FROM AUTHOR]

Abstract Let g E H be the Eguchi–Hanson metric on the blow-up of ℂ 2 at the origin. In this paper we show that m g E H is not balanced for any positive integer m. [ABSTRACT FROM AUTHOR]

Abstract: this paper gives them some properties. This paper firstly introduces rough logic, and proposes factorization of model based on rough logic, and proposes the optimal factorization of model, so one complex model could be factorized into several simple models, which are easy to be handled. this paper not only gives them some properties, but also analyze the time complexity of it. [Copyright &y& Elsevier]

Abstract: This paper firstly introduces rough logic, and proposes factorization of model based on rough logic, and proposes the optimal factorization of model, so one complex model could be factorized into several simple models, which are easy to be handled. this paper gives them somae properties. [Copyright &y& Elsevier]

Abstract: In this paper, we use the exp-function method to construct some new soliton solutions of the Benjamin–Bona–Mahony and modified Benjamin–Bona–Mahony equations. These equations have important and fundamental applications in mathematical physics and engineering sciences. The exp-function method is used to find the soliton solution of a wide class of nonlinear evolution equations with symbolic computation. This method provides the concise and straightforward solution in a very easier way. The results obtained in this paper can be viewed as a refinement and improvement of the previously known results. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the Drazin inverse of a sum of two matrices and derive additive formulas under conditions weaker than those used in some recent papers on the subject. As a corollary we get the main results from the paper of Yang and Liu [H. Yang, X. Liu, The Drazin inverse of the sum of two matrices and its applications, J. Comput. Appl. Math. 235 (2011) 1412–1417]. As an application we give some new representations for the Drazin inverse of a block matrix. [Copyright &y& Elsevier]

Abstract: This paper deals with the pseudo-isochronicity for a class of septic differential systems. In this paper, we transform infinity into the origin so that the properties of infinity can be investigated with the methods developed for finite critical points. By calculating the singular point quantities and period constants of the origin, the problem of infinity being a pseudo-isochronous center has been solved in this case. [Copyright &y& Elsevier]

Abstract: Let be an integer and a bipartite graph with such that . In this paper it has been proved that if for each pair of nonadjacent vertices and , , then for any independent edges of , has a 2-factor with cycles such that and for each . We shall also show that the conditions in this paper are sharp. [Copyright &y& Elsevier]

Abstract: This paper investigates a competitive version of the coloring game on a finite graph . An asymmetric variant of the -relaxed coloring game is called the -relaxed -coloring game. In this game, two players, Alice and Bob, take turns coloring the vertices of a graph , using colors from a set , with . On each turn Alice colors vertices and Bob colors vertices. A color is legal for an uncolored vertex if by coloring with color , the subgraph induced by all the vertices colored with has maximum degree at most . Each player is required to color an uncolored vertex legally on each move. The game ends when there are no remaining uncolored vertices. Alice wins the game if all vertices of the graph are legally colored, Bob wins if at a certain stage there exists an uncolored vertex without a legal color. The -relaxed -game chromatic number, denoted by , of is the least for which Alice has a winning strategy in the -relaxed -coloring game. The -relaxed -coloring game has been well studied and there are many interesting results. For the -relaxed -coloring game, this paper proves that if a graph has an orientation with maximum outdegree and , then for all ; If , then - for all . [Copyright &y& Elsevier]

Abstract: The generalized Petersen graph is an undirected graph on vertices with and . Fiorini claimed to have determined the crossing numbers of and showed all the values of for up to 14, except 12 unknown values. Lovrečič Saražin proved . Richter and Salazar found a gap in Fiorini’s paper, which invalidated his principal results about , and gave the correct proof for . In this paper, we show the crossing numbers of all for up to 16. [Copyright &y& Elsevier]

Abstract: Ecological expert knowledge is often based on qualitative rules consisting of linguistic terms such as ‘low’, ‘moderate’ or ‘high’. Since fuzzy systems transform these rules and terms into a mathematical framework, they allow implementing this expert knowledge in ecological models. However, the development of a reliable knowledge base is complex and time consuming. Recent research has shown that complementing fuzzy systems by data-driven techniques can solve this knowledge acquisition bottleneck. In this paper, a heuristic nearest ascent hill-climbing algorithm for rule base optimisation is applied to construct a fuzzy rule-based habitat suitability model for spawning European grayling (Thymallus thymallus L.) in the Aare river (Bern, Switzerland). Optimisation of the fuzzy rule-based model was based on two different training criteria, the weighted correctly classified instances and Cohen''s Kappa. The ecological relevance of the results was assessed by comparing the optimised rule bases with a rule base derived from ecological expert knowledge. Optimisation based on Kappa appeared to generate acceptable results (CCI=0.70; Kappa=0.32) and was more practical than optimisation based on since the latter required fine tuning of a weight parameter, which accounted for the species prevalence. The optimal rules showed 74% similarity with the rules derived from expert knowledge, while 84% of all model errors was due to false positive predictions of the model. These errors might be due to the impact of variables, which were not included in this study on grayling presence and thus are not necessarily a model error. The habitat suitability model optimised in this paper is able to predict the effect of different impacts on the river system and to select the optimal restoration option. Hence, it could be a valuable decision support tool for river managers and ease the discussion between stakeholders. [Copyright &y& Elsevier]

Abstract: In a recent paper by the authors, Lie bialgebras structures of generalized Virasoro-like type were considered. In this paper, the explicit formula of the quantization of generalized Virasoro-like algebras is presented. [Copyright &y& Elsevier]

Abstract: This paper deals with the qualitative analysis, existence of equilibria and asymptotic behavior of some second-order models of the competition between tumor and immune cells. The background model belongs to d’Onofrio [A. d’Onofrio, A general framework for modeling tumor–immune system competition and immunotherapy: Mathematical analysis and biomedical inferences, Physica D 208 (2005) 220–235; A. d’Onofrio, Tumor–immune system interaction: Modelig the tumor-stimulated proliferation of effectors and immunotherapy, Math. Models Methods Appl. Sci. 16 (2006) 1375–1401]. Various developments proposed in this paper are focussed on the hiding–learning dynamics, followed by the qualitative analysis. [Copyright &y& Elsevier]

Abstract: Intersection types are well known to type theorists mainly for two reasons. Firstly, they type all and only the strongly normalizable lambda terms. Secondly, the intersection type operator is a meta-level operator, that is, there is no direct logical counterpart in the Curry–Howard isomorphism sense. In particular, its meta-level nature implies that it does not correspond to the intuitionistic conjunction. The intersection type system is naturally a type inference system (system à la Curry), but the meta-level nature of the intersection operator does not allow to easily design an equivalent typed system (system à la Church). There are many proposals in the literature to design such systems, but none of them gives an entirely satisfactory answer to the problem. In this paper, we will review the main results in the literature both on the logical interpretation of intersection types and on proposed typed lambda calculi. The core of this paper is a new proposal for a true intersection typed lambda calculus, without any meta-level notion. Namely, any typable term (in the intersection type inference) has a corresponding typed term (which is the same as the untyped term by erasing the type decorations and the typed term constructors) with the same type, and vice versa. The main idea is to introduce a relevant parallel term constructor which corresponds to the intersection type constructor, in such a way that terms in parallel share the same resources, that is, the same context of free typed variables. Three rules allow us to generate all typed terms. The first two rules, Application and Lambda-abstraction, are performed on all the components of a parallel term in a synchronized way. Finally, via the third rule of Local Renaming, once a free typed variable is bounded by lambda-abstraction, each of the terms in parallel can do its local renaming, with type refinement, of that particular resource. [Copyright &y& Elsevier]

Abstract: In this paper, high-resolution finite volume schemes are combined with an adaptive mesh technique inspired by multiresolution analysis to improve the computational efficiency for two-dimensional hyperbolic conservation laws. The method is conservative. Moreover, it is stable which is proven numerically in this paper. The computational grid is dynamically adapted so that higher spatial resolution is automatically allocated to regions where strong gradients are observed. Using this proposed scheme, we compute several two-dimensional model problems and a compressive rate ranging from about 5–10 is observed in all simulations. [Copyright &y& Elsevier]

Abstract: The DPLL procedure is the basis of some of the most successful propositional satisfiability solvers to date. Although originally devised as a proof-procedure for first-order logic, it has been used almost exclusively for propositional logic so far because of its highly inefficient treatment of quantifiers, based on instantiation into ground formulas. The FDPLL calculus by Baumgartner was the first successful attempt to lift the procedure to the first-order level without resorting to ground instantiations. FDPLL lifts to the first-order case the core of the DPLL procedure, the splitting rule, but ignores other aspects of the procedure that, although not necessary for completeness, are crucial for its effectiveness in practice. In this paper, we present a new calculus loosely based on FDPLL that lifts these aspects as well. In addition to being a more faithful lifting of the DPLL procedure, the new calculus contains a more systematic treatment of universal literals, which are crucial to achieve efficiency in practice. The new calculus has been implemented successfully in the Darwin system, described elsewhere. The main results of this paper are theoretical, showing the soundness and completeness of the new calculus. In addition, the paper provides a high-level description of a proof procedure for the calculus, as well as a comparison with other calculi. [Copyright &y& Elsevier]

Abstract: Neighborhoods and neighborhood sequences play important roles in several branches of pattern analysis. In earlier papers in only certain special (e.g. periodic or octagonal) sequences were investigated. In this paper we study neighborhood sequences which are either ultimately periodic or allow at every neighborhood to do nothing at no cost. We give finite procedures and descriptive theoretical criteria for certain important (e.g. metrical) properties of the sequences. Our results are valid for several types of classical neighborhood sequences and for generated distance functions (e.g. octagonal and chamfer distances) which are widely applied in digital image processing. We conclude the paper by showing how our results contribute to the theory of distance transformations. [Copyright &y& Elsevier]

Abstract: This paper describes a generic software designed to implement meshing algorithms based on the Delaunay refinement paradigm. Such a meshing algorithm is generally described through a set of rules guiding the refinement of mesh elements. The central item of the software design is a generic class, called a mesher level, that is able to handle one of the rules guiding the refinement process. Several instantiations of the mesher level class can be stacked and tied together to implement the whole refinement process. As shown in this paper, the design is flexible enough to implement all currently known mesh generation algorithms based on Delaunay refinement. In particular it can be used to generate meshes approximating smooth or piecewise smooth surfaces, as well as to mesh three dimensional domains bounded by such surfaces. It also adapts to algorithms handling small input angles and various refinement criteria. This design highly simplifies the task of implementing Delaunay refinement meshing algorithms. It has been used to implemented several meshing algorithms in the Cgal library. [Copyright &y& Elsevier]

Abstract: In this paper, we study a nondifferentiable minimax fractional programming problem under the assumptions of -invex function. In this paper we utilize the concept of -invexity [M.A. Noor, On generalized preinvex functions and monotonicities, J. Inequalities Pure Appl. Math. 5 (2004) 1–9] and pseudo--invexity [S.K. Mishra, M.A. Noor, On vector variational-like inequality problems, J. Math. Anal. Appl. 311 (2005) 69–75]. We also introduce the concept of strict pseudo--invex and quasi--invex functions. We derive Karush–Kuhn–Tucker-type sufficient optimality conditions and establish weak, strong and converse duality theorems for the problem and its three different dual problems. The results in this paper extend several known results in the literature. [Copyright &y& Elsevier]

Abstract: The considerations of the present paper were inspired by Baksalary [O.M. Baksalary, Idempotency of linear combinations of three idempotent matrices, two of which are disjoint, Linear Algebra Appl. 388 (2004) 67–78] who characterized all situations in which a linear combination , with , , being nonzero complex scalars and , , being nonzero complex idempotent matrices such that two of them, and say, are disjoint, i.e., satisfy condition , is an idempotent matrix. In the present paper, by utilizing different formalism than the one used by Baksalary, the results given in the above mentioned paper are generalized by weakening the assumption expressing the disjointness of and to the commutativity condition . [Copyright &y& Elsevier]

Abstract: We investigate the free complex of a convex geometry. Edelman and Reiner showed that the free complex of a convex geometry is contractible. Moreover, their paper stated a conjecture about the topology of free complexes. This paper proves their conjecture. [Copyright &y& Elsevier]

Abstract: A rank-niche evolution strategy (RNES) algorithm has been developed in this paper to solve unconstrained multiobjective optimization problems. A required number of Pareto-optimal solutions can be generated by the algorithm in a single run. In addition to the operations of recombination, mutation and selection used in original evolution strategy (ES), an external elite set which contains a given number of non-dominated elites is updated and trimmed by a clustering technique to maintain a uniformly distributed Pareto front. The fitness function for each individual contains the information of rank and crowding status. The selection operation using this fitness function considers the superiority and distribution simultaneously. Eight test problems illustrated in other papers are used to test RNES. For some test problems the Pareto-optimal solutions obtained by RNES are better than those obtained by GA-based algorithms. [Copyright &y& Elsevier]

Abstract: Discrete models and continuous control systems are considered in regard to optimality of their trajectories. Some aspects of the principle of optimality [1, p. 83] are analyzed, and it is shown to imply total optimality, that is, the optimality of every part of an optimal trajectory. Certain autonomous systems with free admissible variations possess this property. Nonautonomous optimal systems are not, in general, totally optimal, in which case the principle of optimality is not valid. A modification is proposed for the derivation of the main functional equation to demonstrate that dynamic programming and its functional equations are valid also in the case of nonoptimal remaining trajectories under a certain contiguity condition that is defined and analyzed in the paper. Control systems with incomplete information or structural limitations on controls do not, in general, satisfy the contiguity condition. Control problems for such systems may have optimal solutions which, however, cannot be obtained by dynamic programming. This fact is shown in an example of a widely used engineering system for which an optimal trajectory has all its remaining parts nonoptimal and noncontiguous to the optimal trajectory. The paper presents theoretical justification of dynamic programming for contiguous systems that do not conform to the principle of optimality. Examples are presented to illustrate the results which open new avenues in modeling and optimization of general (not totally optimal) control systems. [Copyright &y& Elsevier]

Abstract: Each member of the family of Gauss hypergeometric functionswhere and z do not depend on n, and (not all equal to zero) satisfies a second order linear difference equation of the formBecause of symmetry relations and functional relations for the Gauss functions, the set of 26 cases (for different values) can be reduced to a set of 5 basic forms of difference equations. In this paper the coefficients , and of these basic forms are given. In addition, domains in the complex z-plane are given where a pair of minimal and dominant solutions of the difference equation have to be identified. The determination of such a pair asks for a detailed study of the asymptotic properties of the Gauss functions for large values of n, and of other Gauss functions outside this group. This will be done in a later paper. [Copyright &y& Elsevier]

Abstract: The topic of the paper is in the field of sculptured surface machining (SSM) on multi-axis NC machines. It presents novel results of investigation of tool-path generation for sculptured surface machining on multi-axis NC machines. The purpose of the paper is to develop an integral form of solution to the problem of optimal tool-path generation. The concept of time-minimal tool-paths is introduced, as well as the optimization problem being formulated analytically. The problem of optimization is subdivided into the following three partial sub-problems: (a) the problem of local tool-path generation; (b) the problem of regional tool-path generation, and finally, (c) the problem of global tool-path generation. The paper presents a closed-form solution to the first two sub-problems. A solution to the problem of optimal tool-path generation is given in the form of an integral equation. The obtained solution enables one to retain the optimal cutter configuration (i.e., the cutter position, and the cutter orientation), as well as the optimal instant direction of feed-rate at every cutter location-point (further, CC-point). [Copyright &y& Elsevier]

Abstract: This paper is devoted to the study of the internal stabilization of the Bernoulli–Euler plate equation in a square. The continuous and the space semi-discretized problems are successively considered and analyzed using a frequency domain approach. For the infinite-dimensional problem, we provide a new proof of the exponential stability result, based on a two-dimensional Ingham''s type result. In the second and main part of the paper, we propose a finite difference space semi-discretization scheme and we prove that this scheme yields a uniform exponential decay rate (with respect to the mesh size). [Copyright &y& Elsevier]

Abstract: The aim of this paper is to define the notions of -valued Lukasiewicz-Moisil algebra of fractions and maximal algebra of fractions taking as a guide-line the elegant construction of a complete ring of fractions by partial morphisms introduced by [Lambek, 1996. Lectures on Rings and Modules, p. 36]. For some informal explanations of the notion of fraction see [Lambek, 1996. Lectures on Rings and Modules, p. 36] In the last part of this paper we prove the existence of a maximal n-valued Lukasiewicz–Moisil algebra of fractions for an n-valued Lukasiewicz–Moisil algebra (Theorem 3.2) and we give an explicit description of this -valued Lukasiewicz–Moisil algebra for some classes of -valued Lukasiewicz–Moisil algebras (finite, chains, Boolean algebras). [Copyright &y& Elsevier]

Abstract: The paper presents modelling of tooth trajectory and process geometry in peripheral milling of curved surfaces. The paper differs from previous work in this area, in two respects. Firstly it deals with milling of variable curvature geometries unlike zero and constant curvature geometries dealt in the past. Secondly true tooth trajectories are considered for modelling process geometry in milling of curved surfaces instead of simpler circular tooth trajectories. Mathematical expressions for, feed per tooth along cutter contact path, entry and exits angles of tooth, undeformed chip thickness and surface error are derived and effect of workpiece curvature on these variables is studied. As cutting forces depend on these process variables, physical experiments were also performed to study the effect of workpiece curvature on cutting forces. Process simulation experiments carried out show the need for modelling true tooth trajectories instead of circular tooth trajectories particularly for curved geometries. Results also show that using simpler constant curvature models to variable curvature geometries for the purpose of estimation of process geometry variables could be erroneous. [Copyright &y& Elsevier]

Data such as real and complex numbers, discrete and continuous time data streams, waveforms, scalar and vector fields, and many other functions, are fundamental for many kinds of computation. In the theory of data, such data types are modelled using topological, or metric, many-sorted algebras and continuous homomorphisms. A theory of such topological data types is needed to answer the general questions:Such a theory seems to be in its infancy: there are many approaches to computability theory on general and specific spaces, and few approaches to specification theory. In some earlier papers, we have studied the questions 1 and 2 with the needs of data type theory in mind, and built a bridge between computations and specifications to try to answer 3. In this paper, we extend and combine several of our results, to prove new theorems thatA technical issue is the localisation of uniform continuity using exhaustions of open sets. We use specifications composed of conditional equations, inequalities and, for convenience, new exhaustion primitives, that define functions uniquely up to isomorphism. [Copyright &y& Elsevier]

The distance d(u,v) from vertex u to vertex v in a digraph G is the length of the shortest directed path from u to v. The eccentricity e(v) of vertex v is the maximum distance of v to any other vertex of G. A vertex u is an eccentric vertex of vertex v if the distance from v to u is equal to the eccentricity of v. The eccentric digraph ED(G) of a digraph G is the digraph that has the same vertex set as G and the arc set defined by: there is an arc from u to v iff v is an eccentric vertex of u. The idea of the eccentric digraph of a graph was introduced by Buckley (Congr. Numer. 149 (2001) 65) and the idea of the eccentric digraph of a digraph by Boland and Miller (Proceedings of AWOCA’01, July 2001, p. 66). In this paper, we examine eccentric digraphs of digraphs for various families of digraphs and we consider the behaviour of an iterated sequence of eccentric digraphs of a digraph. The paper concludes with several open problems. [Copyright &y& Elsevier]

In the pioneering article and two papers, written jointly with McKinsey, Tarski developed the so-called algebraic and topological frameworks for the Intuitionistic Logic and the Lewis modal system. In this paper, we present an outline of modern (non-Lewis) systems with a topological tinge. We consider topological interpretation of basic systems GL and GRZ of the provability logic in terms of the Cantor derivative and the Hausdorff residue. [Copyright &y& Elsevier]

We prove that the equation x2 − kxy + y2 + x = 0 with k ∊ N+ has an infinite number of positive integer solutions x and y if and only if k = 3. For k = 3 the quotient SHAPE="SOL" ALIGN="C" STYLE="S">xy is asymptotically equal to (3 + √5)/2 or (3 − √5)/2. Results of the paper are based on data obtained via Computer Algebra System (derive 5). Some derive procedures presented in the paper made it possible to discover interesting regularities concerning simple continued fractions of certain numbers. [Copyright &y& Elsevier]

In this paper, the following inverse heat conduction problem: ut = uxx, x≥0, t≥0, u(x,0) = 0, x≥0 u(1,t) = g(t), t≥0, u&z.sfnc;x→∞ is bounded, is considered again. This problem is severely ill-posed: its solution (if it exists) does not depend continuously on the data; a small perturbation in the data may cause a dramatically large error in the solution for 0 < x < 1. In this paper, a new wavelet regularization method for this problem is given. Moreover, we can easily find the regularization parameter J such that some sharp stable estimates between the exact solution and the approximate one in Hr(R)-norm meaning is given. [Copyright &y& Elsevier]

Linear feedback shift registers (LFSRs) play a significant role in communications security and we investigate design of a selected class of word-based LFSRs known as σ -LFSRs. Both the search algorithm and the construction algorithm generate efficient primitive σ -LFSRs. The search algorithm first constructs the σ -polynomial and then checks the primitiveness of the σ -polynomial, whereas the construction algorithm for the σ -LFSR, first finds a primitive polynomial f ( x ) and then constructs the primitive σ -LFSR from f ( x ) . In this paper, we present some novel results pertaining to the search algorithm for primitive σ -LFSR along with the exhaustive search space complexity of the search algorithm for σ -LFSRs. Then we investigate and compare the performance of the construction algorithm with the search algorithm for the primitive σ -LFSR. Finally, the number of σ -LFSRs similar to the σ -LFSRs generated by the construction algorithm is provided. [ABSTRACT FROM AUTHOR]

Given a computable ordinal Λ, the transfinite provability logic GLP Λ has for each ξ < Λ a modality [ ξ ] intended to represent a provability predicate within a chain of increasing strength. One possibility is to read [ ξ ] ϕ as ϕ is provable in T using ω-rules of depth at most ξ, where T is a second-order theory extending ACA 0 . In this paper we will formalize such iterations of ω -rules in second-order arithmetic and show how it is a special case of what we call uniform provability predicates. Uniform provability predicates are similar to Ignatiev's strong provability predicates except that they can be iterated transfinitely. Finally, we show that GLP Λ is sound and complete for any uniform provability predicate. [ABSTRACT FROM AUTHOR]

In this paper we continue studying the independent transversal domination number in a graph, i.e., the cardinality of a smallest dominating set which intersects each maximum independent set. As our main result, we prove two upper bounds on the independent transversal domination number in terms of the order and minimum degree of a graph. [ABSTRACT FROM AUTHOR]

The spectrum of a first order sentence is the set of all α such that G ( n , n − α ) does not obey zero–one law with respect to this sentence. In this paper, we prove that the minimal number of quantifier alternations of a first order sentence with infinite spectrum equals 3. We have also proved that the spectrum of a first-order sentence with quantifier depth 4 has no limit points except possibly the points 1 ∕ 2 and 3 ∕ 5 . [ABSTRACT FROM AUTHOR]

In this paper, we establish some scaling invariant regularity criteria for the Navier–Stokes–Maxwell system. [ABSTRACT FROM AUTHOR]